We study the Saffman-Taylor instability of a non-Newtonian fluid in a Hele-Shaw cell. Using a fluid model with shear-rate dependent viscosity, we derive a Darcy’s law whose viscosity depends upon the squared pressure gradient. This yields a natural, nonlinear boundary value problem for the pressure. A model proposed recently by Bonn et al. @Phys. Rev. Lett. 75, 2132 ~1995!# follows from this mo...

Viscoelastic materials with fading memory, e.g., polymers, suspensions, and emulsions, exhibit behavior that is intermediate between the nonlinear hyperbolic response of purely elastic materials and the strongly diffusive, parabolic response of viscous fluids. Many popular numerical methods used in the computation of steady viscoelastic flows fail in important flow regimes, and thus do not capt...

This article is proposed to address the melting heat transfer of a Jeffrey fluid in Blasius and Sakiadis flow caused due to a moving surface. Thermal radiation and a constant free stream are considered in this mathematical model. The non-linear coupled dimensionless equations from the governing equations are attained by employing appropriate similarity transformations. The resulting dimensionle...

Analytical expressions correlating the volumetric flow rate to the inlet and outlet pressures are derived for the time-independent flow of Newtonian fluids in cylindrically-shaped elastic tubes using a one-dimensional Navier-Stokes flow model with two pressure-area constitutive relations. These expressions for elastic tubes are the equivalent of Poiseuille and Poiseuille-type expressions for ri...

In this paper, the unsteady flow of non-Newtonian fluid through a porous medium when an external magnetic field is applied is investigated. The non linear equation of motion is transformed to a similarity differential equation which is solved using the method of successive approximations. The rheological effects are shown and discussed on the velocity profile in terms of rheological parameter o...

We investigate the flow patterns of Newtonian and viscoelastic fluids in microchannels containing bifurcations. The Newtonian fluid used as a reference is de-ionized water, while the non-Newtonian fluid used in the experiments has a shear rheology similar to that of human blood. The geometrical shape of the channels used reproduce bifurcating vessels, typically encountered in microcirculation n...